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Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is μ, a ray, incident at an angle θ, on the face AB would get transmitted through the face AC of the prism provided

Asked in JEE Main 2015 · Total internal reflection and optical fibres

• (1) θ > cos⁻¹[μ sin (A+sin⁻¹(1/μ))]
• (2) θ < cos⁻¹[μ sin (A+sin⁻¹(1/μ))]
• (3) θ > sin⁻¹[μ sin (A-sin⁻¹(1/μ))]
• (4) θ < sin⁻¹[μ sin (A-sin⁻¹(1/μ))]

Step-by-step solution

Why the other options are wrong

• (1) Adds the critical angle to A instead of subtracting it, and uses cosine for Snell's law.
• (2) Adds C to A and also reverses the inequality.
• (4) Reverses the inequality: a smaller θ makes r₂ larger and causes TIR.

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